Copper is a common metal with many important uses, including power generation and building construction. A copper pipe fitting has a mass of 19.7 g and a strand of heavy-duty copper wire has a mass of 84.3 g. Which has the larger specific heat? Which has the larger heat capacity?
The correct answer and explanation is:
Correct Answer:
- Larger Specific Heat: Both have the same specific heat (since they are both made of copper).
- Larger Heat Capacity: The strand of heavy-duty copper wire (because it has more mass).
Explanation (Approx. 300 Words):
When analyzing the heat behavior of substances, two key concepts are specific heat and heat capacity.
Specific Heat (c):
Specific heat is a material property—it tells us how much energy (in joules) is needed to raise the temperature of 1 gram of a substance by 1°C. For copper, this value is approximately: c=0.385 J/g\cdotp°Cc = 0.385\ \text{J/g·°C}
This value does not change based on the size or shape of the copper object. Therefore, both the copper pipe fitting (19.7 g) and the copper wire (84.3 g) have the same specific heat since they are both made of pure copper.
Heat Capacity (C):
Heat capacity, on the other hand, is an extensive property—it depends on the amount of substance. It is calculated as: C=m×cC = m \times c
Where:
- CC = heat capacity,
- mm = mass,
- cc = specific heat.
Let’s compute the heat capacity for each:
- Pipe fitting:
C=19.7 g×0.385 J/g\cdotp°C≈7.58 J/°CC = 19.7\ \text{g} \times 0.385\ \text{J/g·°C} \approx 7.58\ \text{J/°C}
- Copper wire:
C=84.3 g×0.385 J/g\cdotp°C≈32.45 J/°CC = 84.3\ \text{g} \times 0.385\ \text{J/g·°C} \approx 32.45\ \text{J/°C}
So, the copper wire has a larger heat capacity because it has more mass, and therefore it takes more heat to raise its temperature by the same amount.
Conclusion:
- Same specific heat (because material is the same: copper).
- Copper wire has greater heat capacity (because it has greater mass).